What I mean is that they didn’t fully take over the galaxy. They stopped the Empire and Palpatine before they even got to complete their takeover. And no, the First Order doesn’t rule the galaxy in TLJ, if you’re thinking of “The First Order reigns”. The crawl mentions Snoke is sending his legions to seize military control of the galaxy, and Rey herself admits that their takeover is only complete within weeks, implying it isn’t finished.
By saying that, Rey also implies that the First Order’s takeover is inevitable and just a matter of time. That without additional help for the Resistance, the First Order has already basically won and just needs to carry out the formality of assuming total control. And for all intents and purposes, by the start of TLJ, the First Order is the ruling status quo of the Galaxy, with everyone besides the Resistance seemingly accepting of that.
And even disregarding the First Order, there’s also the fact that Luke’s New Jedi Order failed to produce a single new Jedi, let alone a new generation, and that the Republic was essentially a failed state that was incapable of fulfilling even basic defensive functions for itself or its member worlds.